How to move forward or any movement which has surface deform modifier
In your case, the idea is to take what can be "the main" object to drive all the other ones. If we take the force field and make it parent of the plane (flag like) then the force field will be the parent for all:

Select the flag plane then Shift select the force field and CtrlP then choose 'Object'.

Now add a curve, make the force field follow a path, adding this constraint:



The minus X is due to the force field orientation (rotated).

And...



To change the speed, select the curve and change "Frames" (the greater the slower):